This invention relates to a piezoelectric resonator of a thickness-extensional vibration mode, and more particularly to a trapped-energy mode resonator using a piezoelectric ceramic material having a Poisson's ratio of less than one third.
Thickness-extensional mode piezoelectric resonators are composed of a piezoelectric plate which is polarized in the thickness direction and sandwiched between electrodes. In such resonators, however, a number of spurious vibrations are excited near the main resonance as a consequence of mode-coupling with high-order radial vibrations. These spurious responses resulting from contour vibrations can be excluded through a so-called "forward-wave energy-trapping" technique using a partially-electroded piezoelectric plate. In this case, thickness-extensional vibration is confined to an electroded region and does not couple with radial vibrations. To this end, the cutoff frequency is lowered relative to the surrounding region by electrode mass-loading and a piezoelectric effect. This forward-wave energy-trapping technique can be applied to only those piezoelectric materials having a Poisson's ratio of one third or more.
U.S. Pat. No. 3,891,872 discloses a new type of thickness-extensional trapped-energy mode piezoelectric resonator using a piezoelectric plate having a Poisson's ration of less than one third, in which the so-called "backward-wave energy-trapping" technique is used to realize the energy-trapping by slightly reducing the plate thickness locally in the electroded region so as to make a cutoff frequency in the electroded region higher than the cutoff frequency in the surrounding region. However, this technique requires extremely precise control to realize an appropriate thickness ratio between the electroded portion and surrounding region.
Another method of realizing the backward-wave energy-trapping is described in "Energy-Trapping for Backward-Wave Mode Thickness-Vibrations by Controlling Piezoelectric Reaction" in the Transactions of the Institute of Electronics and Communication Engineers of Japan, Vol. J.62-A, No. 1, pp. 8-15 (January 1979) in which a piezoelectric plate of uniform thickness is used and the surrounding region as well as the central trapping region of the plate is electroded, with the electrodes in the surrounding region being short-circuited. The inner and outer electrodes are insulated by an annular unelectroded gap of small width. In addition, a capacitor element is connected in series with the central electrodes. The cutoff frequency at the electroded regions is lowered by the effect of the piezoelectric reaction. However, since the series capacitor reduces the magnitude of the reduction of the cutoff frequency at the control electroded region, the backward-wave energy-trapping can be realized without resorting to the thickness difference of the piezoelectric plate. Although this method facilitates the realization of the backward-wave mode energy-trapping, the usage of an additional capacitor element deteriorates the stability of the resonant frequency due to the difficulty of matching the temperature coefficient of the capacitor element and the piezoelectric plate.